You can do that.
Right click on the files to move -> Library Tools -> Rename, Move & Copy Files
Then play around with the options to get the files to the new location, making sure you use the 'Rename (move files...)' option. This will also ensure the library points to the new location.
The downside is that any folder.jpg cover art will get left behind so you may have to manually tidy up.
Good luck and perhaps test with a few files first to make sure the options are working as you want.